Question 78

If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?

Solution

Let radius of cylinder = 10 cm and height = 10 cm

=> Volume = $$\pi r^2h$$

= $$\pi (10)^2\times10=1000\pi$$

If radius is increased by 25%, => new radius = $$\frac{125}{100}\times10=12.5$$ cm

=> $$\pi r^2h=1000\pi$$

=> $$(12.5)^2h=1000$$

=> $$h=\frac{1000}{156.25}=6.4$$

$$\therefore$$ Decrease in height = $$\frac{(10-6.4)}{10}\times100$$

= $$3.6\times10=36\%$$

=> Ans - (A)

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